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A370630
Lexicographically earliest sequence of distinct positive integers such that the Zeckendorf expansions of two consecutive terms have exactly one common term.
2
1, 4, 3, 11, 8, 9, 6, 5, 7, 2, 10, 12, 14, 13, 15, 16, 18, 17, 20, 23, 21, 22, 19, 25, 26, 24, 27, 29, 28, 30, 35, 33, 37, 32, 38, 34, 36, 31, 41, 42, 39, 43, 47, 40, 44, 48, 45, 49, 46, 52, 60, 53, 56, 51, 58, 50, 59, 55, 57, 54, 61, 63, 62, 64, 68, 65, 69
OFFSET
1,2
COMMENTS
Conjecture: this sequence is a permutation of the positive integers.
FORMULA
A000120(A003714(a(n)), A003714(a(n+1))) = 1.
EXAMPLE
The first terms, alongside the Zeckendorf expansion in binary of a(n), are:
n a(n) z(a(n))
-- ---- -------
1 1 1
2 4 101
3 3 100
4 11 10100
5 8 10000
6 9 10001
7 6 1001
8 5 1000
9 7 1010
10 2 10
11 10 10010
12 12 10101
PROG
(PARI) \\ See Links section.
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, May 01 2024
STATUS
approved